Question

what is the value of a?
a =

Explanation:

Step1: Use the property of congruent triangles

Since the two angles at \(U\) and \(T\) are equal (marked with the same arc), and the triangles are congruent (by ASA or AAS criterion, assume the triangles are congruent based on given angle - side - angle - like markings). In congruent triangles, corresponding sides are equal.

Step2: Identify corresponding sides

The side of length \(15\) in one triangle corresponds to the side of length \(a\) in the other triangle, and the side of length \(9\) corresponds to its corresponding side. But if we consider the side - angle - side (SAS) or other congruence - based side equalities (assuming the triangles are congruent as per the angle markings), we can directly say that \(a = 15\) (because of the congruence of the triangles where the side opposite the equal angles are equal).

Answer:

\(15\)